Obstacle avoidance for discrete-link two-dimensional (2D) hyper-redundant manipulators in known environments is considered. The manipulator is divided into two sections, a proximal section that has not entered the space among obstacles and a distal section among the obstacles. Harmonic potential functions were used, in order to avoid local minima in cluttered environments. A modified panel method is used to generate the potential of any arbitrary shaped obstacle in two-dimensional space. An alternative backbone curve concept and an efficient fitting method are introduced to control the trajectory of proximal links. The fitting method is recursive and avoids the complications involved with solving large systems of nonlinear algebraic equations. Combination of the safe path derived from the harmonic potential field and the backbone curve concept leads to an elegant kinematic control strategy that guarantees obstacle avoidance for planar hyper-redundant robotic manipulators.